Individual Condensation Trails in Aircraft Trajectory Optimization

Project information

Contrail_Foto_lang © Judith Rosenow
Logo_ICATO_large © Judith Rosenow

Contrails are ice clouds formed behind aircraft in a cold and ice-supersaturated atmosphere.

Line-shaped cirrus clouds, which have even been included in the Cloud Atlas by the World Meteorological Society as ‘Cirrus homogenitus’, can cool and warm the Earth-atmosphere radiation system. The dominant effect depends strongly on the lifetime and the microphysical properties of the contrail, as well as on the place and time of formation. In the ICATO project, these conditions are being investigated in detail and the resulting findings are implemented in the TOMATO simulation environment for trajectory optimization.

When do contrails form?
Schmidt-Appleman © Judith Rosenow

Contrails are formed by condensation of atmospheric water vapor on hydrophilic emissions (e.g. soot particles) from the engines. To ensure that the emitted (engine) heat does not prevent condensation, the atmosphere must be very cold. The critical temperature TLM can be calculated using the Schmidt-Appleman criterion: If the straight mixing line intersects the curve of saturation vapor pressure e*, contrails are formed1.

Schmidt-Appleman2 © Judith Rosenow

This temperature criterion depends on the relative humidity U in the atmosphere and is also fulfilled in dry air from a cruising altitude of 10 km.

For contrails to develop into long-lasting cirrus clouds, the atmosphere must also be supersaturated with respect to ice. This happens in the atmosphere (near the tropopause) when there is sufficient water vapor available for natural cloud formation, but no natural condensation nuclei (e.g. salt crystals from seawater, desert sand or flower pollen). Our data analyses from modelled weather data in 2023 have shown a probability of ice supersaturation of 30 % to 50 % in the northern hemisphere.

ISS_Heatmap_ © Judith Rosenow

References

  1. https://www.researchgate.net/publication/262974241_Impact_of_ocean_currents_on_contrail_formation_on_global_scale

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How long do contrails live?

In order to estimate the optical properties of contrails, both their microphysical properties and their lifetime must be determined. Our lifetime model1 calculates the mixing of the contrail with the atmosphere using a sheared Gaussian plume model.

Ice_Particle_Shapes © Judith Rosenow

The ice particle shapes depend on the temperature and the ice particle size increases as it grows into the ice-saturated air. The initial number of ice crystals is determined by the number of soot particles emitted. Subsequently, the crystals can fragment or clump together.

Contrail_Winddrift © Judith Rosenow

During its lifetime, the contrail is pushed in all directions by the wind. If it is not lifted upwards by the wind, the contrail falls downwards due to gravity. If the contrail leaves the ice-saturated layer or the ice water content falls below a critical value, the life of the contrail is over2.

Contrail_Lifetime © Judith Rosenow

This means that the lifespan is largely dependent on the size of the ice-saturated layer and the prevailing winds. Under typical vertical wind conditions, contrails live for several hours even in thin ice-saturated layers2.

References

  1. https://www.researchgate.net/publication/309134708_Modeling_Contrail_life_cycles_based_on_highly_precise_flight_profile_data_of_modern_aircraft

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  2. DOI: 10.3390/su15118669

    a, b

What effect do contrails have on the radiation budget?

Contrails act like a barrier in the Earth-atmosphere radiation balance. They scatter parts of the solar radiation back into the atmosphere (cooling effect). They also absorb and re-emit terrestrial radiation back to the Earth's surface (warming effect). The dominant effect can be determined using a Monte Carlo simulation1.

Strahlungsbilanz © Judith Rosenow
Results_P_net © Judith Rosenow

Due to the strong forward scattering, the optical properties depend not only on the size and number density of the ice crystals, but above all on the solar zenith angle and the intensity of the incoming radiation. The figure shows the radiation balance of contrails [W/(m2)] as a function of the position of the sun and the land use class. A cooling effect is therefore only likely at large solar zenith angles, e.g. during sunrise and sunset.

Sonnenstand_theta © Judith Rosenow

This angle varies in duration depending on the time of year and location. In the mid-latitudes between spring and fall, large angles occur for one to two hours during sunrise and sunset. In winter, large angles occur around midday for five consecutive hours.

References

  1. https://github.com/jro-github/rf-contrails

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Publications
Student theses
  • MA (2023) 3D aircraft trajectory optimization with minimum contrail costs
  • FP (2023) Bedingungen für kühlende Auswirkungen von Kondensstreifen im operationellen Betrieb
  • DA (2024) Modellvergleich und Anwendbarkeitsanalyse globaler Klimamodelle für Luftfahrtemissionen
  • DA (2019): Implementierung einer Berechnungsvorschrift für die Atmosphärische Turbulenz in eine Luftverkehrs-Simulationsumgebung
  • FP (2019): Atmosphärische Turbulenz als Sicherheitsindikator in einer Luftverkehrs-Simulationsumgebung
  • DA (2019): Untersuchung der globalen Verteilung des solaren Strahlungsspektrums
  • FP (2019): Implementierung und Anwendung eines Strahlungstransfermodells zur Berechnung des orts- und zeitabhängigen Strahlungshaushaltes der Erde
  • StA (2014): Modellierung der Rußemission moderner Strahltriebwerke zur Charakterisierung von Kondensstreifen

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Last modified: Sep 18, 2025